On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications [PDF]
Fractional Calculus and Applied AnalysisAbstractWe obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real ...
Maria Alessandra Ragusa +2 more
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An abstract version of the concentration compactness principle [PDF]
Revista Matemática Complutense, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Schindler, I., Tintarev, K.
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Concentration-compactness results for systems in the Heisenberg group [PDF]
Opuscula Mathematica, 2020 In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p,q) critical systems in the Heisenberg group, Adv. Nonlinear Anal.
Patrizia Pucci, Letizia Temperini
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Concentration-compactness principle for variable exponent spaces and applications [PDF]
Electronic Journal of Differential Equations, 2010 In this article, we extend the well-known concentration - compactness principle by Lions to the variable exponent case. We also give some applications to the existence problem for the p(x)-Laplacian with critical growth.
Julian Fernandez Bonder, Analia Silva
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Young measures in a nonlocal phase transition problem [PDF]
, 1997 A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result ...
Winter, M, Ren, X
core +7 more sources
Concentration-compactness principles for Moser–Trudinger inequalities: new results and proofs
Annali Di Matematica Pura Ed Applicata, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrea Cianchi +2 more
exaly +3 more sources
Concentration-compactness principle for nonlocal scalar field equations with critical growth
Journal of Mathematical Analysis and Applications, 2017 The aim of this paper is to study a concentration-compactness principle for homogeneous fractional Sobolev space $\mathcal{D}^{s,2} (\mathbb{R}^N)$ for ...
João Marcos do Ó, Diego Ferraz
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A Remark on the Concentration Compactness Principle in Critical Dimension [PDF]
Communications on Pure and Applied Mathematics, 2021 AbstractWe prove some refinements of the concentration compactness principle for Sobolev space W1, n on a smooth compact Riemannian manifold of dimension n. As an application, we extend Aubin's theorem for functions on with zero first‐order moments of the area element to the higher‐order moments case.
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we
Dong-Lun Wu
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The Existence Result for a p-Kirchhoff-Type Problem Involving Critical Sobolev Exponent
Journal of Function Spaces, 2023 In this paper, by using the mountain pass theorem and the concentration compactness principle, we prove the existence of a positive solution for a p-Kirchhoff-type problem with critical Sobolev exponent.
Hayat Benchira +3 more
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